Drs. Roderic Phibbs, William Mentzer and Kevin Shannon are working together with pediatricians at 10 large medical centers on a research study to give recombinant human erythropoietin to premature babies. Premature babies are often anemic and require blood transfusions to increase their red blood cell counts. This research study seeks to determine whether administration of erythropoietin will stimulate these babies to produce their own red blood cells.